December 7, 2015

The Question

How did the MLPA affect fish densities in the Channel Islands?

The Channel Islands

MLPA Monitoring

  • Since 2003, MPA and "reference" sites surveyed
  • Stratified random placement of survey sites
  • SCUBA transect visual surveys
  • Canopy, column, bottom
  • Count, identify, measure fish
  • Record environmental conditions

Identification Strategy

Difference in Difference

  • Treatment: MLPA == Mariel Boatlift
  • Treated: Fished == Miami ; Unfished == New Orleans

Difference-in-Difference

  • Key Assumption: parallel trends pre-treatment

Model

  • We have a problem…

Model

  • Usual method doesn't work…
  • So after taking a week to figure that out…
  • Going with "hurdle" or delta method
  • Data are nested by
    • fish species f
    • site-side s
    • year y

\(P(y) = ...\)

\(P(y = 0)\) if \(y = 0\)

\(( 1 - P(y = 0)) P(y)\) if \(y > 0\)

Model

Presence/Absence

  • GLM with logit-link

\[p_{f,s,y} = \gamma_{1}fished_{f} + \gamma_{2}mpa_{s,y} + \gamma_{3}FxM_{f,s,y} +\]

\[\sum\gamma_{4}year_{y} + \sum\gamma_{5}trophic_{f} + \gamma_{6}linf_{f} + \]

\[ \gamma_{7}temperature_{s,y} + \gamma_{8}visibility_{s,y}\]

Model

Observed

  • Good old fashioned linear regression

\[ d_{f,s,y} = \beta_{1}fished_{f} + \beta_{2}mpa_{s,y} + \beta_{3}FxM_{f,s,y} + \sum\beta_{4}region_{s} + \]

\[ \sum\beta_{5}trophic_{f} + \beta_{6}yearsmpa_{s,y} + \beta_{7}FxYM_{f,s,y} + \]

\[+ \beta_{7}linf_{f} + \beta_{8}vbk_{f} + \beta_{9}temp_{s,y} + \beta_{10}vis_{s,y} + \]

\[ \beta_{11}templag1_{s,y} + \beta_{12}templag2_{s,y} + \beta_{13}templag3_{s,y} + \beta_{14}templag4_{s,y} + \]

\[\beta_{15} + \sum\beta_{16}year_{y} \]

Likelihood

\[ \sum [dbinom(o_{f,s,y},1,\hat{p_{f,s,y}}, log = T) + \] \[ dnorm(d_{f,s,y},\hat{d_{f,s,y}},\sigma, log = T])^{o_{f,s,y}} ] \]

Priors

  • Lots of priors to deal with here…

  • For now assuming uniform priors on most things except…

  • Yeary ~\(N(0,\sigma^{y})\)
  • \(\sigma^{y}\) ~\(TN(0.1,0.2)\)
  • Yearyp ~\(N(0,\sigma^{y,b})\)
  • \(\sigma^{y,b}\) ~\(TN(0.1,0.2)\)
  • Regionr ~\(N(0,\sigma^{r})\)
  • \(\sigma^{r}\) ~\(TN(0.1,0.2)\)

  • \(\sigma\) ~\(TN(0.1,0.2)\)

Diagnostics

MCMC

  • Runs are preliminary

Diagnostics

MCMC

Diagnostics

MCMC

  • R2 of 0.15

Diagnostics

Regression

  • Looks normal!

Results

  • Treatment on the treated is insignificant
  • MPAs take a while to kick in?

Results

  • Considering the hurdle model

Results

  • Thinking of this as CPUE…
  • Recruitment pulse in 2009?

Conclusions

  • No significant effect of presence/absence of MPAs on fished species

  • Over time the MLPA increased fished species density

  • MPAs are noisy

Next Steps

  • The demon is slow!

  • Improved hierarchychal structure
    • Species blocking?

  • What does hurdle model do to identification?

  • Compare to
    • Propensity scores
    • MPA/Reference using South and Central coast data

Thanks!

Model

  • Tobit model common solution to zero-truncated data
  • requires normality

Diagnostics

Hurdle

Hurdle component seems reasonable

Diagnostics

Regression